1. Technical Field
This invention relates in general to communications and, more particularly, to an 8PSK modulator.
2. Description of the Related Art
Currently, there are several modulation techniques used for wireless communications. One such technique is 8PSK modulation, which uses a modulation symbol rate of 1/Ts=1625/6 Ksymbols/sec (approximately 270.833 Ksymbols/sec), which corresponds to 3+1625/6 Kbits/sec (i.e., 812 Kbits/sec). Ts is the symbol period.
Modulation bits are Gray mapped in groups of three to 8PSK symbols by the rule: Si=ej2πL/8, where L is given by Table 1.
TABLE 1Gray mappingModulating BitsParameter L(1, 1, 1)0(0, 1, 1)1(0, 1, 0)2(0, 0, 0)3(0, 0, 1)4(1, 0, 1)5(1, 0, 0)6(1, 1, 0)7
The 8PSK Gray mapping of modulating bits of Table 1 in an IQ plane is shown in FIG. 1.
The 8PSK symbols are continuously rotated with 3π/8 radians per symbol before pulse shaping. The rotated symbols are defined as S′i=Sieji3π/8, where i=0, 1, 2, 3 . . . . This rotation prevents origin crossing in the IQ plane.
Pulse shaping is performed as follows:
      c    0    =      {                                                                                                            ∏                                          i                      =                      0                                        3                                    ⁢                                                                          ⁢                                      S                    ⁡                                          (                                              t                        +                                                  iT                          s                                                                    )                                                                      ,                                                                                      for                  ⁢                                                                          ⁢                  0                                ≤                t                ≤                                  5                  ⁢                                      T                    s                                                                                                                          0                ,                                                    else                                      ⁢                                  ⁢                  S          ⁡                      (            t            )                              =              {                                                                              sin                  ⁡                                      (                                          π                      ⁢                                                                        ∫                          0                          t                                                ⁢                                                                              g                            ⁡                                                          (                                                              t                                ′                                                            )                                                                                ⁢                                                                                                          ⁢                                                      ⅆ                                                          t                              ′                                                                                                                                            )                                                  ,                                                                                      for                  ⁢                                                                          ⁢                  0                                ≤                t                ≤                                  4                  ⁢                                      T                    s                                                                                                                                            sin                  ⁡                                      (                                                                  π                        2                                            -                                              π                        ⁢                                                                              ∫                            0                                                          t                              -                                                              4                                ⁢                                                                  T                                  s                                                                                                                                              ⁢                                                                                    g                              ⁡                                                              (                                                                  t                                  ′                                                                )                                                                                      ⁢                                                                                                                  ⁢                                                          ⅆ                                                              t                                ′                                                                                                                                                                          )                                                  ,                                                                                      for                  ⁢                                                                          ⁢                  4                  ⁢                                      T                    s                                                  <                t                ≤                                  8                  ⁢                                      T                    s                                                                                                                          0                ,                                                    else                                          
FIG. 2 illustrates c0 and FIG. 3 illustrates S(t).
The baseband signal is defined as
      y    ⁡          (      t      )        =            ∑      i        ⁢                  S        i        ′            ⁢                                    c            0                    ⁡                      (                          t              -              iT                        )                          .            The modulated RF (radio frequency) carrier during the useful part of the burst is defined as
            x      ⁡              (                  t          ′                )              =                                        2            ⁢                          E              s                                            T            s                              ⁢              Re        ⁡                  [                                    y              ⁡                              (                                  t                  ′                                )                                      ·                          ⅇ                              j                ⁡                                  (                                                            2                      ⁢                      π                      ⁢                                                                                          ⁢                                              f                        0                                            ⁢                                              t                        ′                                                              +                                          φ                      0                                                        )                                                              ]                      ,where Es is the energy per modulating symbol, f0 is the center frequency, and φ0 is a random phase, which is constant during one burst.
The calculations for 8PSK modulation can be very processor intensive. Therefore, a need has arisen for an efficiently performing 8PSK modulation.